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Hint: It's not as difficult as it seems. It's the number of ways the friends can form a circle divided by the number of ways the names can be drawn out of the hat.
1/10

For a group of n friends, there are n! (n factorial) ways to draw the names out of the hat. Since a circle does not have a beginning and end, choose one person as the beginning and end of the circle. There are now (n-1)! ways to distribute the remaining people around the circle. Thus the probability of forming a single circle is

(n-1)! / n!

Since n! = (n-1)! * n (for n > 1), this can be rewritten as

(n-1)! / (n*(n-1)!)

Factoring out the (n-1)! from the numerator and denominator leaves

1/n

as the probability.
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Giving You Your Sight

Hint:
An eye
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White And Brittle

Hint:
They are bones
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Different Shapes And Sizes

Hint:
Bones
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Soccer Kick Riddle

Hint:
Ever heard of gravity? She kicked it up.
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Ticking In Its Weary Pace

Hint:
Big Ben. The clock in London.
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Unwilling To Kiss

Hint:
A spider.
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Dont Trust The Ocean

Hint:
There was something fishy about it.
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School Ladder Riddle

Hint:
Because it was high school
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Bedtime With Monsters Riddle

Hint:
It was afraid there were kids under the bed.
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Eskimo Toys Riddle

Hint:
With igloo
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Falling Thespians Riddle

Hint:
It was just a stage he was going through!
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The Queen And The Duke

Hint:
The Queen said that: "Until you see me again you shall not reveal to anyone what happen to me." The face of the Queen is on the money.
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A Piece On A Chessboard

Hint:
The queen
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The Head Of A Hive

Hint:
Queen
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